Rolling Manifolds of Different Dimensions
نویسندگان
چکیده
منابع مشابه
Rolling Stiefel manifolds
In this paper rolling maps for real Stiefel manifolds are studied. Real Stiefel manifolds being the set of all orthonormal k-frames of an n-dimensional real Euclidean space are compact manifolds. They are considered here as rigid bodies embedded in a suitable Euclidean space such that the corresponding Euclidean group acts on the rigid body by rotations and translations in the usual way. We der...
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For a complete Riemannian manifold M with compact boundary ∂M denote by C∂M the cut locus of ∂M in M . The rolling radius of M is Roll(M) := dist(∂M, C∂M ). Let Focal(∂M) be the focal distance of ∂M in M . Then conditions are given that imply the equality Roll(M) = Focal(∂M). This generalizes Blaschke’s rolling theorem from bounded convex domains in Euclidean space to more general Euclidean dom...
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We consider sufficient conditions of local removability of coincidences of maps f, g : N → M, where M, N are manifolds with dimensions dimN ≥ dimM. The coincidence index is the only obstruction to the removability for maps with fibers either acyclic or homeomorphic to spheres of certain dimensions. We also address the normalization property of the index and coincidence-producing maps.
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ژورنال
عنوان ژورنال: Acta Applicandae Mathematicae
سال: 2014
ISSN: 0167-8019,1572-9036
DOI: 10.1007/s10440-014-9972-2